DEPARTMENT OF COMPUTER SCIENCE SAMPLE QUESTIONS Mathematical aptitude 1) How many 4’s immediately proceded by 5 but not immediately followed by 1 are there in the following series of numbers? 5,4,8,1,4,9,5,4,1,1,4,5,5,4,6,5,4,7,5,4,7,3,2,4,7 a) 2 b) 3 c) 4 d) 5 2) 16 X 85 = 8651, what is 73 X 42? a) 4372 b) 3723 c) 4327 d) 4732 3) Find the wrong term in the following series 3,4,10,32,136,685,4116 a) 136 b)10 c)4116 d)32 4) In the figure below, ABCD is a rectangle, and DE and CF are arcs of circles centered at A and B. What is the area of the stripped region? 5 D C 2 A a) 10 – π E F B b) 2(5 – π) c) 2(5 – 2π) d) 5(2 – π) 5) Find the value of (1/10 +1)10. 6) In a small get together there are total 28 handshakes exchanged. Find number of guests in the party. Physics 7) A solid cylinder of mass M rolls without slipping on an inclined plane inclined at angle θ. Find the linear acceleration of the cylinder. 8) Implement the Boolean function f(A,B,C)=AB+BC+AC using NAND gate only. 9) Find the current flow across 2R resistance. 4R R E 2R Mathematics 10) Show that a2 + 10 ab ac ab b2 + 10 bc ac bc c2+10 is divisible by 100. 11) Solve: xy = yx and x=2y. 12) 17. Let X is a set containing K elements and let Y be a set containing N elements. How many functions are there from X to Y? How many one to one functions from X to Y are there? Mathematical Puzzle 13) There is a number, the second digit of which is smaller than its first digit by 4 and if the number is divided by the digit sum, the quotient will be 7. Can you find the number? 14) Twenty five dots are arranged in a square formation in 5 rows and 5 columns a shown in sketch. Can you connect 12 of these dots with straight lines to form a perfect cross which has five dots inside and 8 dots outside?